Analysis of variance applied to determinations of equilibrium constants

The statistical analysis of variance has been applied to the values of the equilibrium constants of the glycinate-proton and glycinate-nickel systems, determined in different laboratories by pH-titration in aqueous solution. The analysis shows how the main part of the error derives from the variability from one titration to another even in the same laboratory. Therefore the data for a single titration (k) must be processed separately, thus yielding a mean value for the equilibrium constant logbeta (pqr)(k) of the species M(p)H(q)L(r); from these mean values for different titrations in each laboratory l, a within-laboratory grand average, logbeta (pqr)(l), can be calculated; the variance of this grand average measures the experimental error. A further analysis of the data from the different participating laboratories shows that there were no significant differences between laboratories for the constants reported. From these results it can be inferred that all the values of the mean constants logbeta (pqr)(k) for one species, as determined separately for each titration in four laboratories, belong to the same population. A chi(2) analysis of these populations demonstrates that the stability constants of the species HL, H(2)L(+), NiL(+), NiL(2) (with L(-) = glycinate) are normally distributed, but not that for NiL(-)(3). Therefore, general mean values of the first four constants can be calculated and proposed as reliable standard values at 25 degrees and I = 1.0M Na(Cl): protonation of glycinate, log beta(011) = 9.651(12), log beta(021) = 12.071(26); nickel-glycinate complexes, log beta(101) = 5.615(35), log beta(102) = 10.363(62). These values indicate that the standard deviations are rather higher than those often reported in the literature.